This paper revisits the problem of multiagent consensus from a graph signal processing perspective. Describing a consensus protocol as a graph spectrum filter, we present an effective new approach to the analysis and design of consensus protocols in the graph spectrum domain for the uncertain networks, which are difficult to handle by the existing time-domain methods. This novel approach has led to the following new results: 1) explicit connection between the time-varying consensus protocol and the graph filter; 2) new necessary and sufficient conditions for both finite-time and asymptotic average consensus of multiagent systems (MASs); 3) direct link between the consensus convergence rate and periodic consensus protocols, and conversion of fast consensus problem to the polynomial design of the graph filter; 4) two explicit design methods of the periodic consensus protocols with a predictable convergence rate for MASs on uncertain graphs; and 5) explicit formulas for the convergence rate of designed protocols. Several numerical examples are given to demonstrate the validity, effectiveness, and advantages of these results.Index Terms-Average consensus, graph filter, graph signal processing (GSP), multiagent systems (MASs).
I. INTRODUCTIONC ONSENSUS of multiagent systems (MASs) is a fundamental problem in collective behaviors of autonomous individuals, which has been extensively studied in the last decades [1]-[5]. The key problem is to design appropriate distributed protocols (control sequences) such that each agent only get information from its local neighbors, and the whole network of agents may coordinate to reach an agreement on certain quantities of interest eventually. Many results have been Manuscript
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.